In researching your problem a I came across this DuoTherm troubleshooting document that may not apply to your model, but that notes that Dometic does NOT use a standard telephone 4 wire connection cable from the thermostat to the roof control box. It LOOKS like your standard telephone connect cable, but that has 2 wires flipped in the wiring. The Dometic version has pin 1 connecting to pin1 on the other end et cetera. Telephone cables flip pins 2 and 3, I believe. Also, I keep seeing mention of the DIP switch array on the AC control board. You might want to research what the correct settings of the DIP switches are for your application.
Did you have installation instructions with your new unit? You might want to carefully review these, since that's when your problems seemed to begin.
Good Luck!!!